$(999)^2 - (998)^2 = x$

### Concept & Formula This problem is a direct, straightforward application of the algebraic identity for the difference of two perfect squares. $$a^2 - b^2 = (a - b)(a + b)$$ ### Step-by-Step Solution * Identify the terms from the equation, where $a = 999$ and $b = 998$. * Substitute these values directly into the algebraic identity: $$(999)^2 - (998)^2 = (999 - 998)(999 + 998)$$ * Simplify the mathematical terms inside the parentheses: $$(1)(1997)$$ * Multiply the final results: $$1997$$ ### Exam Strategy & Shortcut Whenever you are subtracting the squares of two consecutive numbers (meaning $a - b = 1$), the final answer is always simply the sum of those two numbers. Instantly perform $999 + 998 = 1997$ in your head to save time. ### Common Pitfall Students often attempt to manually calculate the massive square of 999 and 998 individually. This is a massive time sink and highly prone to calculation errors. ### Final Answer Therefore, the correct answer is **1997**.